The only way you would get a substantial current draw from the starter is if the solenoid was pulling in and making contact. In this case, you would get a solid "thump" from the starter, which can easily be heard from the driver's seat. If you're getting "nothing" from the starter, then the...
There are 2 connections to the starter. A small push on connector (logic from the ignition switch circuit) and a bolt on terminal which is a direct connection to the battery positive terminal.